David,
Assume you're the same as sent me a mail?
From your mail and this thread it seems you're just taking up MTBing as a student with the aim of racing/competing as part of your studies, and on a tight budget.
My initial advice would be;
1. Get your hair cut - it's cheaper than an expensive helmet
2. I'd strongly suggest you get out and have a go on a MTB before you take the plunge in buying a bike. You don't say what sort of competition your interested in but there are several areas you can get into from Cross Country, Trailquest, 4X and Downhilling each requiring a slightly different focus on what bike you choose. Dalby Forest has some good hire bikes.
3. £500 should be plenty to get something decent but shop around, try a few out and haggle hard - never pay the full asking price. Take a look at our front page and the local dealers that Clifton members get discount at and go and get some advise from them. Better to pay a little more for the right size/type of bike than click on a nice picture on the internet and get something delivered you weren't expecting.
4. Your basic equipment list sounds good, but you don't list a waterproof which is essential. If you're intending doing some hard rides I'd consider making sure your bike can carry a waterbottle. Carry energy drink in your waterbottle and water in your camelback. Add to your list 2 spare tubes, a multitool, a descent pump and some gloves. Don't be afraid to hunt through bargain bins. Your kit soon loses its shine on a MTB anyway.
5. If you're unsure about what you're buying or dealing/haggling with a bikeshop don't be afraid to ask for help.
6.
http://www.ashcycles.com/power/ are another good source for knock down prices on decent bikes, they're also a proper shop rather than just a warehouse. Someone in the club has just bought a Kona from them reduced from £1700 to <£750 and it's perfect, just last year's colour. They seem to have a constant changing stock so maybe worth giving them a ring to see what they have in.
7. Like road riding most of your success in competition will be down to experience, skill and your fitness, not your bike. You're coming into it at the right time as the racing season doesn't really start again until Spring which will give you several months to work on all 3. Your road bike will prove invaluable through winter for improving your fitness and riding with a club will help with motivation.
Good luck and keep us posted!